Empirical Verification of a Short-Coil Correction Factor

Kennedy, Mark William; Akhtar, Saleem; Bakken, Jon Arne; Aune, Ragnhild E.

doi:10.1109/tie.2013.2281168

Cited by 16 publications

(14 citation statements)

References 12 publications

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“…The authors in Ref. [7] introduce a frequency dependent (or temperature dependent) Nagaoka correction factor and verify its accuracy experimentally for different frequency ranges and sample materials. In this work we assume that the correction factor is a nonlinear function of temperature, which we determine numerically by calibrating the model with the experiments.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The modified Nagaoka coefficient we consider in the model is Kn′=αTKn where αT is a temperature dependent parameter, which is found by calibrating the model with the experiments. This approach is more general and practical than the approach presented in Ref [7]. αT includes many other relevant influencing factors like geometry corrections (imperfections, complex shapes), material uncertainties, and boundary conditions.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…In principle, this parameter is temperature dependent and it changes during the heating process. However, its explicit functionality is not well known apart from some conjectures [7]. Therefore, we allow the optimization of this parameter by calibrating the model to the measurement data.…”

Section: Introductionmentioning

confidence: 99%

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Inverse Model for the Control of Induction Heat Treatments

et al. 2019

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In this work, we present and test an approach based on an inverse model applicable to the control of induction heat treatments. The inverse model is comprised of a simplified analytical forward model trained with experiments to predict and control the temperature of a location in a cylindrical sample starting from any initial temperature. We solve the coupled nonlinear electromagnetic-thermal problem, which contains a temperature dependent parameter α to correct the electromagnetic field on the surface of a cylinder, and as a result effectively the modeled temperature elsewhere in the sample. A calibrated model to the measurement data applied with the process information such as the operating power level, current, frequency, and temperature provides the basic ingredients to construct an inverse model toolbox, which finally enables us to conduct experiments with more specific goals. The input set values of the power supply, i.e., the power levels in the test rig control system, are determined within an iterative framework to reach specific target temperatures in prescribed times. We verify the concept on an induction heating test rig and provide two examples to illustrate the approach. The advantages of the method lie in its simplicity, computationally cost effectiveness and independence of a prior knowledge of the internal structure of power supplies.

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Section: Mathematical Modelmentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

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Inverse Model for the Control of Induction Heat Treatments

et al. 2019

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“…X g is the air gap reactance. These parameters are estimated by using following formulations [9,10] graphite crucible, respectively, A c is the effective area (m 2 )o f induction coil, k n and k * n are the short coil and modified kNagaoka correction factors ((4) suggested by Vaughan and Williamson,(5) suggested by Kennedy), respectively, k r is the coil inter-turn space factor.…”

Section: Analytical Formulationmentioning

confidence: 99%

Analytical, numerical and experimental analysis of induction heating of graphite crucible for melting of non‐magnetic materials

Patidar

Hussain

Jha

et al. 2017

IET Electric Power Applications

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This study presents analytical formulation used for design of helical coil for induction heating of solid and hollow cylindrical non-magnetic workpiece (graphite crucible). This formulation is applied for estimation of the active power in graphite crucibles and reactive power drawn by the induction coil in presence of different wall thickness (30, 20, 10 and 5 mm) of graphite crucibles at different frequency (1-50 kHz). Magnetic field produced by induction coil is estimated by using empirical factors suggested by kNagaoka et al. Induction heating processes, i.e. electromagnetism and heat transfer physics are mathematically modelled by Maxwell and Fourier equations, respectively. Finite-element method is used to solve the electromagnetic field in frequency domain and heat transfer in transient domain. Numerical analysis is carried out by using two-dimensional axisymmetric geometry. Analytical results and numerical results are compared and are found to be in good agreement with each other. Experimentally obtained coil voltage and graphite crucible temperature were compared with numerical results and the authors found that they also match very well confirming the validity of their assumptions in analytical/numerical approach.

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“…The analytical derivation of the time-averaged Lorentz forces for helical coils is presented in the Appendix, and the key equations have also been published and discussed elsewhere [16,17]. The required correction factors for "Short" coils [18] are currently available only as an average along the entire length of the coil, making it impossible to accurately estimate the forces as a function of axial position. However, the analytical solution is still a highly useful tool to evaluate the overall accuracy of any numerical Lorentz force modelling [16], and if combined with drag coefficients or Stokes' law it can be used to determine magnitudes for particle migration velocities, at least in the absence of MHD effects.…”

Section: Electromagnetophoresis Theorymentioning

confidence: 99%

Impact of Coil Geometry on Magnetohydrodynamic Flow in Liquid Aluminium and Its Relevance to Inclusion Separation by Electromagnetophoresis

Kennedy¹,

Bakken

Aune³

2015

Journal for Manufacturing Science and Production

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Magnetohydrodynamic (MHD) flow will be produced in liquid aluminium by gradients in the Lorentz forces created by the interactions of induced currents and the time-varying magnetic field of an induction coil. The magnitude of the velocity field is driven by the curl of the Lorentz forces. Practical coils are "Short" and produce magnetic fields having both lower flux densities and Lorentz forces than very "Long" or infinite coils. Unlike infinite coils, the magnetic fields of "Short" coils contain both axial and radial components, which vary with position and thereby produce powerful MHD mixing. When such a coil is used with the objective of achieving nonconductive particle migration in a liquid metal by electromagnetophoresis, the obtained mixing effects can be highly detrimental. In the present study different coil geometries and induced Lorentz forces with resulting MHD mixing are modelled (COMSOL ® 4.4), and the obtained Lorentz forces compared to analytical results.

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Empirical Verification of a Short-Coil Correction Factor

Cited by 16 publications

References 12 publications

Inverse Model for the Control of Induction Heat Treatments

Inverse Model for the Control of Induction Heat Treatments

Analytical, numerical and experimental analysis of induction heating of graphite crucible for melting of non‐magnetic materials

Impact of Coil Geometry on Magnetohydrodynamic Flow in Liquid Aluminium and Its Relevance to Inclusion Separation by Electromagnetophoresis

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